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A vernier callipers has 1 mm marks on the main scale. It has 20 equal divisions on the vernier scale which match with 16 main scale divisions. For this vernier calipers, the least count is

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Important Questions on Units and Measurements

MEDIUM

Physics>Mechanics>Units and Measurements>Measurement of Length

In a vernier callipers, each

cm

on the main scale is divided into

20

equal parts. If

10^{t h}

vernier scale division coincides with

9^{t h}

main scale division. Then the value of vernier constant will be _____

\times 10^{- 2} mm

MEDIUM

Physics>Mechanics>Units and Measurements>Measurement of Length

Diameter of a steel ball is measured using a Vernier calipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its Vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as:

S.No.	MS (cm)	VS divisions
1.	0.5	8
2.	0.5	4
3.	0.5	6

If the zero error is - 0.03 cm, then mean corrected diameter is:

MEDIUM

Physics>Mechanics>Units and Measurements>Measurement of Length

The smallest division on the main scale of a Vernier calipers is $0.1 cm$ . Ten divisions of the Vernier scale correspond to nine divisions of the main scale. The figure below on the left shows the reading of this calipers with no gap between its two jaws. The figure on the right shows the reading with a solid sphere held between the jaws. The correct diameter of the sphere is

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EASY

Physics>Mechanics>Units and Measurements>Measurement of Length

The figure of a centimetre scale below shows a particular position of the Vernier calipers. In this position, the value of $x$ shown in the figure is (figure is not to scale):

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HARD

Physics>Mechanics>Units and Measurements>Measurement of Length

The diameter of a cylinder is measured using a vernier callipers with no zero error. It is found that the zero of the vernier scale lies between

5.10 cm

and

5.15 cm

of the main scale. The vernier scale has

50

divisions equivalent to

2.45 cm

. The

24^{th}

division of the vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is,

HARD

Physics>Mechanics>Units and Measurements>Measurement of Length

The one division of main scale of vernier callipers reads

1 mm

and

10

divisions of Vernier scale is equal to the

9

divisions on main scale. When the two jaws of the instrument touch each other the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between

4.1 cm

and

4.2 cm

and

6^{th}

Vernier division coincides with a main scale division. The diameter of the bob will be _____

10^{- 2} cm

MEDIUM

Physics>Mechanics>Units and Measurements>Measurement of Length

The diameter of a spherical bob is measured using a vernier callipers.

9

divisions of the main scale, in the vernier callipers, are equal to

10

divisions of vernier scale. One main scale division is

1 mm .

The main scale reading is

10 mm

and

8^{th}

division of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of

0.04 cm,

then the radius of the bob is _____________

\times 10^{- 2} cm .

MEDIUM

Physics>Mechanics>Units and Measurements>Measurement of Length

In an experiment with vernier callipers of least count

0.1 mm

, when two jaws are joined together the zero of vernier scale lies right to the zero of the main scale and

6^{th}

division of vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between

3.2 cm

and

3.3 cm

marks and

4^{th}

division of vernier scale coincides with the main scale division. The diameter of bob is measured as

HARD

Physics>Mechanics>Units and Measurements>Measurement of Length

A specially designed Vernier caliper has the main scale least count of

1 mm

. On the Vernier scale, there are 10 equal divisions and they match with 11 main scale divisions. Then, the least count of the Vernier caliper is:

EASY

Physics>Mechanics>Units and Measurements>Measurement of Length

The vernier scale used for measurement has a positive zero error of $0.2 mm .$ If while taking a measurement it was noted that $0$ on the vernier scale lies between $8.5 cm$ and $8.6 cm$ . Vernier coincidence is $6,$ then the correct value of measurement is $cm .$

(least count $= 0.01 cm$ )

EASY

Physics>Mechanics>Units and Measurements>Measurement of Length

A travelling microscope has

20

divisions per

cm

on the main scale while its Vernier scale has total

50

divisions and

25

Vernier scale divisions are equal to

24

main scale divisions, what is the least count of the travelling microscope ?

HARD

Physics>Mechanics>Units and Measurements>Measurement of Length

Consider a Vernier calipers in which each

1 cm

on the main scale is divided into

8

equal divisions and a screw gauge with

100

divisions on its circular scale. In the Vernier calipers,

5

divisions of the Vernier scale coincide with

4

divisions on the main scale and in the screw gauge, one complete rotation of the circular scale moves it by two divisions on the linear scale. Then:

MEDIUM

Physics>Mechanics>Units and Measurements>Measurement of Length

In a Vernier Caliper

10

divisions of Vernier scale is equal to the

9

divisions of main scale. When both jaws of Vernier Calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and

4^{th}

Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to

1 mm

. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between

30

and

31

divisions of main scale reading and

6^{th}

Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be:

MEDIUM

Physics>Mechanics>Units and Measurements>Measurement of Length

The Vernier constant of Vernier callipers is

0.1 mm

and it has zero error of

(- 0.05 cm)

. While measuring diameter of a sphere, the main scale reading is

1.7 cm

and coinciding vernier division is

5

. The corrected diameter will be _____

\times 10^{- 2} cm

EASY

Physics>Mechanics>Units and Measurements>Measurement of Length

The Vernier scale of a travelling microscope has

50

divisions which coincides with

49

main scale divisions. If each main scale division is

0.5 mm

, then the least count of the microscope is

MEDIUM

Physics>Mechanics>Units and Measurements>Measurement of Length

The pitch and the number of divisions, on the circular scale, for a given screw gauge are

0.5 mm

and

100

respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies

3

divisions below the mean line.

The readings of the main scale and the circular scale, for a thin sheet, are

5 .5 mm

and

48

respectively, the thickness of this sheet is:

MEDIUM

Physics>Mechanics>Units and Measurements>Measurement of Length

The least count of the main scale of a screw gauge is

1 mm .

The minimum number of divisions on its circular scale required to measure

5 μm

diameter of a wire is:

MEDIUM

Physics>Mechanics>Units and Measurements>Measurement of Length

One main scale division of a vernier callipers is

a

cm

and

n^{th}

division of the vernier scale coincide with

{(n - 1)}^{th}

division of the main scale. The least count of the callipers in

mm

is :

EASY

Physics>Mechanics>Units and Measurements>Measurement of Length

The least count of the main scale of a vernier calipers is

1 mm

. Its vernier scale is divided into

10

divisions and coincide with

9

divisions of the main scale. When jaws are touching each other, the

7^{th}

division of the vernier scale coincides with a division of the main scale and the zero of vernier scale is lying right side of the zero of the main scale. When this vernier is used to measure the length of the cylinder the zero of the vernier scale between

3.1 cm

and

3.2 cm

and

4^{th}

VSD coincides with the main scale division. The length of the cylinder is (VSD is vernier scale division)

HARD

Physics>Mechanics>Units and Measurements>Measurement of Length

There are two vernier calipers both of which have $1 cm$ divided into $10$ equal divisions on the main scale. The Vernier scale of one of the calipers $(C_{1})$ has $10$ equal divisions that correspond to $9$ main scale divisions. The Vernier scale of the other caliper $(C_{2})$ has $10$ equal divisions that correspond to $11$ main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in $cm$ ) by calipers $C_{1}$ and $C_{2}$ respectively, are

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A vernier callipers has 1 mm marks on the main scale. It has 20 equal divisions on the vernier scale which match with 16 main scale divisions. For this vernier calipers, the least count is

Important Questions on Units and Measurements

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